A SINGLE-FACTOR ASSET MARKET

Single Factor Model

βi = index of a securities’ particular return to the factor
M = unanticipated movement commonly related to security returns
Ei = unexpected event relevant only to this security
Assumption: a broad market index like the S&P500 is the common factor

Specification of a Single-Index Model of Security Returns
Use the S&P 500 as a market proxy
Excess return can now be stated as:

This specifies the both market and firm risk

Figure 6.11 Scatter Diagram for Dell

Figure 6.12 Various Scatter Diagrams

Components of Risk
Market or systematic risk: risk related to the macro economic factor or market index
Unsystematic or firm specific risk:  risk not related to the macro factor or market index
Total risk = Systematic + Unsystematic

Measuring Components of Risk

si2 = bi2 sm2 + s2(ei)
    where;
si2 = total variance
bi2 sm2 = systematic variance
s2(ei) = unsystematic variance

*s=std. deviation

Examining Percentage of Variance

Total Risk = Systematic Risk + Unsystematic Risk
Systematic Risk/Total Risk = p2
    ßi2 s m2 / s2 = p2
    bi2 sm2 / bi2 sm2 + s2(ei) = p2

Advantages of the Single Index Model

Reduces the number of inputs for diversification
Easier for security analysts to specialize